求解高次方程的一个异步并行迭代算法  

Asynchronous Parallel Iterative Algorithm Solving Equation of Higher Degree

作　　者：杨本立[1] 李安志[1] 曾宪雯[1] 韩卫华[1] 

机构地区：[1]中国工程物理研究院职工工学院,四川绵阳621900

出　　处：《西南交通大学学报》2004年第5期679-683,共5页Journal of Southwest Jiaotong University

摘　　要：用高次方程正项分解方法,将求解实系数高次方程非零实数根的问题,转化成求解两单调上升凹函数在平面直角系第一象限内交点横坐标的等价问题;给出了基于共享存储多指令流多数据流(MIMD)并行计算模型求解任意实系数高次方程全部实数根的大范围收敛性异步并行迭代算法,并分析了算法计算的复杂程度.By using the method for positive term resolution of equations of higher degree, all non-zero real roots of a real coefficient equation of higher degree were obtained by determining the abscissas of intersection points of two monotonically increasing concave functions in the first quadrant of a planar rectangular coordinate system. An asynchronous parallel iterative algorithm based on the shared memory MIMD (multiple instruction and multiple data streams) parallel computation model was put forward. This iterative algorithm has the characteristic of global convergence and can be used to determine all the real roots of any real coefficient equation of higher degree. In addition, the complexity of the algorithm was discussed.

关 键 词：高次方程 正项分解 大范围收敛性迭代算法 异步并行迭代算法 

分 类 号：O246[理学—计算数学] O241.7[理学—数学]